Answers
===============================================================
Explanation:
The given stem and leaf plot leads to this data set
68,68,69,69
71,72,77,77,78,78
80,81
I broke it up to have each tens digit get its own row. That way it's bit more readable.
Unfortunately, the term "average" in math is very vague. It could mean one of the following
meanmedianmodeTo get the mean (specifically the arithmetic mean), we will add up the values and then divide by n = 12 because there are 12 values in the list above. Adding said values gets us
68+68+69+69+71+72+77+77+78+78+80+81 = 888
Dividing that over 12 then leads to 888/12 = 74
The arithmetic mean is 74.
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To get the median, we would first sort the data set. Though that is already done for us. From here, we locate the middle-most item.
Since there are n = 12 items here, the middle item is between slot n/2 = 12/2 = 6 and slot 7
The values in slots 6 and 7 are 72 and 77 respectively. The midpoint of those values is (72+77)/2 = 149/2 = 74.5
The median is 74.5
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The mode is possibly the quickest measure of center or average we can compute. We simply look at the value that shows up the most. In this case, the following values show up twice (which is the most frequent of all the values)
68697778They are all tied for the title of "mode". It's possible to have more than one mode, so we say the mode is the set {68,69,77,78}.
Due to the nature of multiple modes, the mode is often not a good measure of center (but it's still a possibility; especially for categorical data).
In this case, I think the mean or median is a better measure of center.
Since there aren't any outliers, the mean is the best measure of center in this case. Luckily, the mean and median (74 and 74.5 respectively) are fairly close to one another.
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To summarize everything, the term "average" is too vague and it could refer to the mean, median or mode. In this problem, the mean is possibly the best measure of center since there aren't any outliers and the mode isn't one single value.
We found the following:
mean = 74median = 74.5mode = {68,69,77,78}It's very likely your teacher is wanting the mean.
Related Questions
Which of the following is equivalent to 0 equals 3 x squared minus 12 x minus 15 when completing the square?
Answers
x = 5, -1
Step-by-step explanation:
0 = 3x^2 - 12x - 15 or
3x^2 - 12x - 15 = 0
By solving for x, use the Quadratic Formula.
… x = 5 and/or -1
After completing the square the quadratic equation [tex]3x^{2} -12x-15=0[/tex] is equivalent to [tex](x-2)^2=3^2[/tex].
What is a quadratic equation?"It is a polynomial equation with degree two."
What is completing the square method?"It is a method that is used for converting a quadratic expression of the form [tex]ax^2 + bx + c[/tex] to [tex]a(x - h)^2 + k[/tex] "
For given example,
We have been given a quadratic equation.
[tex]3x^{2} -12x-15=0[/tex]
First we divide above quadratic equation by 3,
[tex]x^{2} -4x-5=0\\\\x^2-4x=5[/tex] ................(i)
Now for completing the square first find [tex](\frac{-b}{2a} )[/tex]
[tex]\frac{-b}{2a}\\=\frac{-(-4)}{(2)(1)}\\\\ =\frac{4}{2}\\\\ =2[/tex]
Add [tex](\frac{-b}{2a} )^2[/tex] on both the sides of equation (i),
[tex]x^{2} -4x+4=5+4\\\\(x-2)^2=9\\\\(x-2)^2=3^2[/tex]
Therefore, after completing the square the quadratic equation [tex]3x^{2} -12x-15=0[/tex] is equivalent to [tex](x-2)^2=3^2[/tex].
Learn more about completing the square here:
https://brainly.com/question/4822356
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14. The area of 10 square plots is 160 ares. Find the length in metres of the side of each plot (3mks)
Answers
Answer:
Step-by-step explanation:
1 are = 100 m²
Assuming the ten squares are congruent, the area of each square is 160/10 = 16 are
16 are × 100 m²/are = 1600 m²
each side is √1600 = 40 m
The length of side of plot is 40 meters.
What is area?The total space occupied by a flat (2-D) surface or shape of an object is known as area.
Draw a square on a piece of paper with a pencil. It has two dimensions. The term "area" refers to the area that the shape occupies on the paper.
Now picture your square as being comprised of smaller unit squares. The number of unit squares required to cover a 2-D shape's total surface area is used to calculate its area.
Given the area of 10 square plot is 160 are,
here 1 are = 100 m²
area of 10 square plot = 160 x 100 = 16,000 m²
area of 1 square plot = 16000/10 = 1600 m²
area of square is "a²"
where a is side of square
area = a² = 1600 m²
a = √1600
a = 40 m
Hence the length of side of each plot is 40 meters.
Learn more about area;
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What sum of money, invested at 9%
interest per year, is needed to provide an
income of $45 per year?
Answers
Answer:
$500
Step-by-step explanation:
Intrest = P. A * Intrest Rate * Time
Time = 1 year, Intrest Rate = 9%, P. A. is what we need to find, Intrest is 45
45=x*9/100*1, x=500
Answer:
500
Step-by-step explanation:
I = PRT where I is the interest, P is the amount invested, R is the rate and T is the time
We want 1 year at 9% to get 45 dollars in interest
45 = P ( .09) (1)
45 = .09P
Divide each side by .09
45/ .09 = P
500 =P
Help only #31,33, please thank you
Answers
Answer:
31) 4d + 28 33) 10 + 5
Step-by-step explanation:
31) 4 ( d + 7) = 4 x 7 = 28 = 4d + 28
33) 5 ( 2m + 1 ) = 5. 2m + 5 . 1: 10m + 5
In 20P4 how many choices are
there for vice-president from a
state of four officers?
Note: The vice president is the second officer
to be elected.
Acellus
Answers
Explanation:
There are 20 choices for president, and 20-1 = 19 choices for vice president. You count down by 1 each time you fill a seat. So that means you'll have 19-1 = 18 choices for the third seat, and 18-1 = 17 choices for the fourth seat.
What is the value of the expression, written in standard form?
Answers
Answer:
200
Step-by-step explanation:
6.6/3.3 = 2
10^-2 - (-4) = 10^2
The answer is 2 * 10^2 or 200.
Fewer and fewer customers have been coming into the restaurant, so Bill, the manager, decides to change the entire menu. After he does this, he finds out that people loved the food, but the service has been driving people away. This represents what kind of problem in the decision-making process? O a) Failure to develop enough options O b) Failure to correctly define the problem c) Failure to act on a decision O d) Failure to evaluate the decision
Answers
Answer:
failure to correctly define the problem
Step-by-step explanation:
He changes the menu without identify that the real problem was the service.
Expand (2+x)^-3
....
Answers
Answer:
1/(x^3 + 6x^2 + 12x + 8)
Step-by-step explanation:
The first thing we do is rationalize this expression. (2+x)^-3 is written as
1/(2+x)^3
Then from there we can foil out the denominator. It is easiest to foil (2+x)(2+x) first and then multiply that product by (2+x).
(2+x)(2+x) = 4 + 4x + x^2
(4+4x+x^2)(2+x) = 8+8x+2x^2+4x+4x^2+x^3.
Then we combine like terms and put them in order to get:
x^3 + 6x^2 + 12x + 8
And of course we can't forget that this was raised to the negative third power, so our answer is 1/(x^3 + 6x^2 + 12x + 8)
Answer:
Hello,
Step-by-step explanation:
[tex](a+x)^n=a^n+\left(\begin{array}{c}n\\ 1\end{array}\right)*a^{n-1}*x+\left(\begin{array}{c}n\\ 2\end{array}\right)*a^{n-2}*x^2+\left(\begin{array}{c}n\\ 3\end{array}\right)*a^{n-3}*x^3+\left(\begin{array}{c}n\\ 4\end{array}\right)*a^{n-4}*x^4+...+\left(\begin{array}{c}n\\ n\end{array}\right)*a^{n-n}*x^n[/tex]
[tex]with \\\\\left(\begin{array}{c}n\\ 1\end{array}\right)=n\\\\\left(\begin{array}{c}n\\ 2\end{array}\right)=\dfrac{n(n-1)}{2!} \\\\\left(\begin{array}{c}n\\3 \end{array}\right)=\dfrac{n(n-1)(n-2)}{3!} \\\\...\\[/tex]
[tex]\dfrac{1}{(2+x)^3} =\dfrac{1}{8} +3*\dfrac{x}{4}+3\dfrac{x^2}{2}+x^3\\\\[/tex]
f(x) = x - 1. Find the inverse of f(x).
Answers
Answer:
f^-1 (x) = x+1
Step-by-step explanation:
f(x) = x-1
y = x-1
Exchange x and y
x = y-1
Solve for y
Add 1 to each side
x+1 = y-1+1
x+1 = y
The inverse is x+1
f^-1 (x) = x+1
Find the lengths of the other two sides of the isosceles right triangle
Answers
Answer:
h²=p²+b²
(7√2)²=x²+x²
(49×2)=2x²
2x²=49ײ
x²=49×2/2
x²=49
x=√49=7
x=7
OAmalOHopeO
which function is positive for the entire interval (-3,-2)
Answers
Answer:
There can be several such functions; however, the basic condition that needs to be met for a function to be positive for the interval [–3, –2] is that it should be multiplied by (-1) Hence, one such function that is positive for the entire interval is f(x) = -x
Step-by-step explanation:
6. How many rational number are there Between ⅕and⁹/⁵
Answers
9514 1404 393
Answer:
an infinite number
Step-by-step explanation:
Between any pair of numbers, there are ...
an infinite number of rational numbers, and
an infinite number of irrational numbers
A rectangle auditorium seats 1260 people. The number of seats in each row exceeds the number of rows by 12. Find the number of seats in each row
Answers
Answer:
Easy, all you ha
Step-by-step explanation:
What is the total cost of a $28 pair of jeans if the sales tax is 7.5%?
Answers
Answer:
30.10
Step-by-step explanation:
First find the amount of tax
28 * 7.5%
28 * .075
2.10
Add this to the price of the pants
28+2.10 =30.10
help pls!!! Classify the following question: “President, vice president, and secretary are being chosen for the Environmental Club. In how many different ways can these three offices be filled from a list of ten members?”
Answers
the answer is: combation
[tex] \frac{2}{4} + 5 \times 36 + 2 \frac{6}{3 } = [/tex]
what is answer
Answers
Step-by-step explanation:
[tex] \frac{2}{4} + 5 \times 36 + 2 \frac{6}{3} [/tex]
[tex] = \frac{1}{2} + 180 + 2 \times \frac{2}{1} [/tex]
[tex] = \frac{1}{2} + 180 + 4[/tex]
[tex] = \frac{1 + 360 + 8}{2} [/tex]
[tex] = \frac{369}{2} [/tex]
[tex] = 184 \frac{1}{2} \: or \: 184.5(ans)[/tex]
Find the probability. A calculator requires a keystroke assembly and a logic circuit. Assume that 75% of the keystroke assemblies and 94% of the logic circuits are satisfactory. Find the probability that a finished calculator will be satisfactory.
Answers
Answer:
0.705 = 70.5% probability that a finished calculator will be satisfactory.
Step-by-step explanation:
Probability of independent events:
If two events, A and B, are independent, the probability of both happening is the multiplication of the probabilities of each happening, that is:
[tex]P(A \cap B) = P(A)P(B)[/tex]
In this question:
Event A: Keystroke assembly are satisfactory.
Event B: Logic circuits are satisfactory.
75% of the keystroke assemblies and 94% of the logic circuits are satisfactory.
This means that [tex]P(A) = 0.75, P(B) = 0.94[/tex]
Find the probability that a finished calculator will be satisfactory.
Both satisfactory, and since they are independent:
[tex]P(A \cap B) = P(A)P(B) = 0.75*0.94 = 0.705[/tex]
0.705 = 70.5% probability that a finished calculator will be satisfactory.
if x = -5
x2 + 3
x - 2
Answers
Answer:
Step-by-step explanation:
Write the phrase as an algebraic expression: 3 less than 4 times a number
Answers
Answer:
4x-3 is the expression to your question
Answer:
3[tex]\leq[/tex]4x
Step-by-step explanation:
Can someone check my answers if they are correct or incorrect? If it is incorrect, please let me know why it is incorrect please.
Answers
Find a homogeneous second-order Cauchy-Euler equation with real coefficients if the given number is a root of its auxiliary equation.
mi= i
C1cos(ln(x)) + C2sin(ln(x))
Answers
I'm going to assume that you mean to say that i = √(-1) is a root of the auxiliary equation. That is, if the Cauchy-Euler DE is
x ²y'' + axy' + by = 0
then the auxiliary equation obtained by substituting y = xᵐ is
x ² (m (m - 1) xᵐ ⁻ ²) + ax (m xᵐ ⁻ ¹) + bxᵐ = 0
which reduces to
m (m - 1) + am + b = 0
or
m ² + (a - 1) m + b = 0
By the fundamental theorem of algebra, we can write the quadratic in terms of its roots r₁ and r₂,
(m - r₁) (m - r₂) = 0
Given that one root is the imaginary unit i, and the coefficients of the aux. equation are real, it follows that the other root is -i, because complex roots must occur with their conjugates. So we have as our aux. equation,
(m - i ) (m + i ) = 0
or
m ² + 1 = 0
Then a - 1 = 0 and b = 1, so that the given root and general solution correspond to the DE,
x ²y'' + xy' + y = 0
Copy center charges $0.08 a page for machine fed copies and $0.20 for hand fed copies.If Logan's bill for 80 copies of his movie script is $13, how many copies of each type were made?
Answers
Answer:
machine fed copies = 25, hand fed copies = 55
Step-by-step explanation:
let machine fed = x, hand fed = y
0.08x+0.2y = 13 (1)
x+y = 80
x= 80-y (2)
sub (2) into (1)
0.08(80-y)+0.2y=13
6.4-0.08y+0.2y=13
0.12y=6.6
y = 55
sub y=55 into eqn 2
x = 80-55 = 25
At what points do these graphs intersect
y=x²-x-6
y=x+2
Answers
Answer:
Solve algebraicallyEliminate y:
x² - x - 6 = x + 2x² - 2x = 8x² - 2x + 1 = 9(x - 1)² = 3²1) x - 1 = 3 ⇒ x = 4 ⇒ y = 62) x - 1 = -3 ⇒ x = -2 ⇒ y = 0The solution is:
(-2, 0), (4, 6)Solve graphicallySee the attached
Answer:
[tex]thank \: you[/tex]
Correct the formula
Please
Answers
Answer:
The addition should be divided by 4 and not 3 since there are 4 meals.
Step-by-step explanation:
round 12.5478 to the nearest hundredths
Answers
Answer:
12.04
Step-by-step explanation:
Find the number in the hundredth place 4 and look one place to the right for the rounding digit 1 . Round up if this number is greater than or equal to 5 and round down if it is less than 5 .
Find the L.C.M. of: a2 + 2a +1, a? + 3a + 2
Answers
Step-by-step explanation:
sorrry .......................
Which of the following are exterior angles? Check all that apply.
Answers
Answer:
<5
Step-by-step explanation:
exterior angles + the corresponding interior angle of the triangle = 180º or a straight angle
the only exterior angle shown in the diagram is <5, which corresponds to the interior <2
hope this helps!
Answer:
<5
Step-by-step explanation:
everything else is matched up perfectly so it has to be <5
Can you please help me
Answers
Answer:
Step-by-step explanation:
⅝ - 5/9 = 5/72
How many solutions on the interval {0, 2020} sin 2x + 1 + sin x + cos x have?
Answers
Answer:
0
Step-by-step explanation:
Instructions are in the picture
Answers
Answer:
123123 3213123 12312 dasdsd aw dasd sda asdasd
Step-by-step explanation:
